Polynomial division modulo 5, gcd of two polynomials
I have to find the gcd $h$ of $f$ and $g$ in $\mathbb{F}_5[X]$. $f=X^9+X^8+X^7+X^6+X^5+X^4+X^3+X^2+X+1,$ $g=X^4+X-2.$ Here is my polynomial division: My s...
Published: Sep 06, 2026
Prove that an isometry preserves straight lines using intuitive geometry
This is an exercise of the book "Basic Mathematics" by Serge Lang, p.145. I've been working on this proof for a few days and I can't seem to mak...
Published: Sep 06, 2026
What makes the Cauchy principal value the "correct" value for a integral?
I haven't been able to find a good answer to this searching around online. There is a related old question here, but it never received much attention...
Published: Sep 06, 2026
Calculating expected value and variance of a probability density function
If I was given a probability density function: $$f(y) = \left\{\begin{array}{ll}\frac{3y^2(4-y)}{64} & \textrm{for } 0 \leq y \leq 4\\ 0 & \textrm...
Published: Sep 06, 2026
Prove Taylor expansion with mean value theorem
http://vapour-trail.blogspot.com/2006/03/brief-explanation-of-taylor-series-via.html provides an intuitive derivation of Taylor expansions from the mean v...
Published: Sep 06, 2026
How to find the exact value of the cosine of 50 degree angle
I want to know the exact value of $\cos 50^\circ$. Actually I have already tried lot of times to solve but I cannot find the exact value of $\cos 50^\circ$.
Published: Sep 06, 2026
Calculating the coordinates of end terminal point of an arc from known r, arc in radyan and starting terminal point coordinates of the arc.
I have searched the site and found similar questions of mine but not exaclty I needed. I have an arc. I know the coordinates of the arc center (P0), r (ra...
Published: Sep 06, 2026
More comprehensive General Topology's book than Engelking
Other than Engelking General Topology, I also come across other graduate general topology text such as Dugundji and Kelley, which I also find them interes...
Published: Sep 06, 2026
Solve for $X$ in matrix equation
How can I solve for $X$ in this matrix equation? $$\begin{bmatrix}-3&-8\\-9&5\end{bmatrix} X + \begin{bmatrix}4&-7\\3&-2\end{bmatrix} = \b...
Published: Sep 06, 2026
Why is this answer wrong? (point of intersection between parabola and line)
Question: Use the discriminant to determine the number of points of intersection of the line $y=3x+5$ and the quadratic functions $f(x)=3x^2-2x-4$. Solve ...
Published: Sep 06, 2026
